If the image of $\left(\frac{-7}{5}, \frac{-6}{5}\right)$ in a line is $(1, 2)$,then the equation of the line is

$A$ small quantity of solution containing $Na^{24}$ radio nuclide of activity $1 \, \mu Ci$ is injected into the blood of a person. $A$ sample of the blood of volume $1 \, cm^3$ taken after $5 \, hours$ shows an activity of $296$ disintegrations per minute. What will be the total volume of the blood in the body of the person? Assume that the radioactive solution mixes uniformly in the blood of the person. (Take $1 \, Ci = 3.7 \times 10^{10} \, dps$ and $e^{-\lambda t} = 0.7927$; where $\lambda$ = disintegration constant)

If $f$ is a differentiable function such that $f(2x+1) = f(1-2x)$ for all $x \in R$,then what is the minimum number of roots of the equation $f'(x) = 0$ in the interval $x \in (-5, 10)$,given that $f(2) = f(5) = f(10)$?

Work done in increasing the size of a soap bubble from a radius of $3\, cm$ to $5\, cm$ is nearly (Surface tension of soap solution $= 0.03\, Nm^{-1}$) (in $\pi \,mJ$)

$A$ conducting rod with resistance $r$ per unit length is moving inside a vertical magnetic field $\vec B$ at constant speed $v$ on two horizontal parallel ideal conductor rails. The ends of the rails are connected to a resistor $R$. The separation between the rails is $d$. The rod maintains a tilted angle $\theta$ to the rails. Find the external force required to keep the rod moving.